Does brew print `Updating Homebrew...` even when it is not updating?

I have set HOMEBREW_AUTO_UPDATE_SECS:

$ printenv HOMEBREW_AUTO_UPDATE_SECS
604800

But I always see the Updating Homebrew....

Well, I have HOMEBREW_AUTO_UPDATE_SECS set to 86400, but I can’t say for sure that brew updates more often than per 24 hours (in my case).

Try to set HOMEBREW_NO_AUTO_UPDATE to 1 and check if it do update.